Résumé: The classical Whitney approximation theorem states that a smooth function function f: Rn - R can be approximated by analytic functions. We prove that these analytic functions approximating f can be taken aas real holomorphic functions on the whole space Cn.
Mots-clés: Whitney approximation theorem; Approximation by analytic functions
Résumé: En esta memoria se obtienen resultados de dependencia continua respecto a variaciones del dominio y condiciones de frontera, de los autovalores y autofunciones principales de problemas lineales de valores en la frontera sujetos a condiciones de frontera mixtas muy generales, así como de las soluciones positivas de ciertos problemas semilineales elipticos bajo las mismas condiciones de frontera. También se analiza el comportamiento
asintótico de dichas soluciones cuando ciertos potenciales en la frontera del domino explotan.
Résumé: We prove that any divisor Y of a global analytic set X subset of R(n) has a generic equation, that is, there is an analytic function vanishing on Y with multiplicity one along each irreducible component of Y. We also prove that there are functions with arbitrary multiplicities along Y. The main result states that if X is pure dimensional, Y is locally principal,
X \ Y is not connected and Y represents the zero class in H(q-1)(infinity) (X, Z(2)) then the divisor Y is globally principal.
Résumé: Escape to infinity is proved to occur when a charge moves under the action of the magnetic field created by a finite number of planar closed wires.
Mots-clés: Escape to infinity, Magnetic field, Lorentz equation
Résumé: The invariant p(V ) has been introduced by M. Marshall as a measure of the complexity of semialgebraic sets of a real algebraic variety V . This invariant is defined as the least integer such that every semialgebraic set S ⊂ V has a
separating family with p(V ) polynomials.
In this paper we provide estimates for the invariant p in the case of analytic set germs. One of the tools we use is a realization theorem which
Résumé: Let X subset of R-n be a coherent analytic surface. We show that the connected components of global analytic subsets of X are global and we compute the stability index and Brocker's t-invariant of X. We also state a real Nullstellensatz for normal surfaces.
Mots-clés: Coherent surfaces, real analytic sets, analytic functions.
Résumé: Submersions f such that f(-1)(0) contains a given fiber F, and that are invariant under a family of vector fields s leaving F invariant, are constructed. Examples for which a submersion of this kind cannot exist are also given. In the absence of a geometric theory of submersions f invariant under s, most of our treatment is analytic.
Résumé: We solve the 17th Hilbert Problem and prove the Artin-Lang property for normal real analytic surfaces. Then we deduce that the absolute (resp. relative) holomorphy ring of such a surface consists of all bounded (resp. locally bounded) meromorphic functions.
Mots-clés: Real analytic surfaces; Meromorphic functions.
Département: Fac. de CC. Matemáticas - Depto. de Geometría y Topología; Fac. de CC. Matemáticas - Depto. de Álgebra; Fac. de CC. Matemáticas - Instituto de Matemática Interdisciplinar (IMI)
